Everything Maths Grade 10

37.A(2; 4),B(4;2)andC(4; 0)are the vertices of△ABC.DandE(1; 2)are the mid-points ofAB

andACrespectively.

A

B

C

E

D

x

y

a)Find the gradient ofBC.

b)Show that the coordinates ofD, the mid-point ofABare(3; 1).

c)Find the length ofDE.

d)Find the gradient ofDE. Make a conjecture regarding linesBCandDE.

e)Determine the equation ofBC.

38.In the diagram pointsP(3; 3),Q(1;2),R(5; 1)andS(x;y)are the vertices of a parallelogram.

 4  2 2 4 6

 2

2

4

6

P

Q

R

S

T

x

y

M

a)Calculate the length ofP Q.

b)Find the coordinates ofMwhere the diagonals meet.

c)FindT, the mid-point ofP Q.

d)Show thatM T∥QR.

e)Calculate the coordinates ofS.

39.The coordinates of△P QRare as follows:P(5; 1),Q(1; 3)andR(1;2).

a)Through calculation, determine whether the triangle is equilateral, isosceles or scalene. Be sure to

show all your working.

b)Find the coordinates of pointsSandT, the mid-points ofP QandQR.

c)Determine the gradient of the lineST.

d)Prove thatST∥P R.

324 8.5. Chapter summary